Guignard’s Constraint Qualification (GCQ) and Multiobjective Optimisation Problems
Guignard’s Constraint Qualification (GCQ) and Multiobjective Optimisation Problems作者机构：Department of Mathematics University of Chittagong Chattogram Bangladesh
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2022年第10卷第7期
页 面：2356-2367页
学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学]
主 题：Constraint Qualifications Multiobjective Optimization Karush Kuhn-Tucker Conditions Constraint Optimization
摘 要：Investigation of optimality conditions has been one of the most interesting topics in the theory of multiobjective optimisation problems (MOP). To derive necessary optimality conditions of MOP, we consider assumptions called constraints qualifications. It is recognised that Guignard Constraint Qualification (GCQ) is the most efficient and general assumption for scalar objective optimisation problems;however, GCQ does not ensure Karush-Kuhn Tucker (KKT) necessary conditions for multiobjective optimisation problems. In this paper, we investigate the reasons behind that GCQ are not allowed to derive KKT conditions in multiobjective optimisation problems. Furthermore, we propose additional assumptions that allow one to use GCQ to derive necessary conditions for multiobjective optimisation problems. Finally, we also include sufficient conditions for multiobjective optimisation problems.
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